Transportation engineering, as a practical engineering discipline, relies heavily on the accurate calibration of importation parameters from field data. In the real world, most transport relations possess inherent non-linearity. Two prevailing methods for handling non-linear regression are the non-linear least-squares method (LSM) with an iterative solution, and linearisation for the non-linear regression function. The second method applies a linear regression method to solve the non-linear regression problem but requires a data transformation of the observations from variant coordinates, and the objective function is suspected to be changed accordingly. This work describes the authors’ investigation into the problem of non-linear regression through two illustrative examples, the calibration of three non-linear (either exponential or logarithmic) single-regime models for fundamental diagram and the regression of non-linear (power) bunker-consumption model, by applying the weighted LSM (WLSM) and the ordinary LSM to calibrate. It is found that linearising the regression model leads to deviations, and the data transformation can create even more concern with the WLSM because the weights can be redistributed after the data transformation. A further investigation into the linear regression and the non-linear regression gives more suggestions on the choice of regression method.

中文翻译：

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数据驱动运输研究的线性化研究：两个代表性案例研究

运输工程作为一门实用的工程学科，在很大程度上取决于对来自现场数据的输入参数的准确校准。在现实世界中，大多数运输关系都具有固有的非线性。用于处理非线性回归的两种主要方法是带有迭代解的非线性最小二乘法（LSM），以及用于非线性回归函数的线性化。第二种方法应用线性回归方法来解决非线性回归问题，但是需要根据变体坐标对观测值进行数据转换，并且怀疑目标函数会相应更改。这项工作通过两个示例性的例子来描述作者对非线性回归问题的研究，通过使用加权LSM（WLSM）和普通LSM进行校准，对基本图的三个非线性（指数或对数）单区域模型进行校准以及非线性（功率）燃油消耗模型的回归。发现线性化回归模型会导致偏差，并且数据转换会引起WLSM的更多关注，因为可以在数据转换后重新分配权重。对线性回归和非线性回归的进一步研究为回归方法的选择提供了更多建议。发现线性化回归模型会导致偏差，并且数据转换会引起WLSM的更多关注，因为可以在数据转换后重新分配权重。对线性回归和非线性回归的进一步研究为回归方法的选择提供了更多建议。发现线性化回归模型会导致偏差，并且数据转换会引起WLSM的更多关注，因为可以在数据转换后重新分配权重。对线性回归和非线性回归的进一步研究为回归方法的选择提供了更多建议。